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Determination of the characteristic parameters in the special collinear space in the general case

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Author(s): Krasić Šonja | Marković Miroslav

Journal: Facta Universitatis - series : Architecture and Civil Engineering
ISSN 0354-4605

Volume: 5;
Issue: 1;
Start page: 49;
Date: 2007;
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Keywords: special collinear spaces | vanishing planes | axes | foci and directrix planes of space

ABSTRACT
The projective space consists of the finitely and infinitely distant elements. The special collinear spaces in the general case, are set with five pairs of biunivocally associated points, so the quadrangle in the first space obtained by the three principal and one penetration point of the remaining two through the plane of the first three identical or similar to the associated quadrangle obtained in the same way in the second space. In order to associate two special collinear spaces, it is necessary to determine the following characteristic parameters: vanishing planes, space axes (principal normal lines), foci (apexes of the associated identical bundles of straight lines) and directrix plane (associated identical fields of points). The paper is based on constructive processing of the special collinear spaces in the general case. The structural methods which are used are Descriptive Geometry (a pair of Mange's projections) and Projective geometry.
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